- #1
songoku
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Homework Statement
Let
p: x and y satisfy inequality x2 + y2 + 4x - 8y + c < 0 where c is real number
q: x and y satisfy x - y + 8 > 0 ; 4x + 3y - 24 < 0 ; y < 0
Find the range of c so that:
a. p is sufficient condition for q
b. p is necessary condition for q
Homework Equations
Circle
Inequality
The Attempt at a Solution
p is the region inside circle (excluding circumference), centered at (-2, 4) and has radius of √(20 - c)
q is the infinite region bounded by two lines and x - axis
I want to ask whether my opinion is correct:
a. For p to be sufficient condition for q, region q should be located inside the circle
b. For p to be necessary condition for q, the circle should be inside the region of q
Thanks